3.11.82 \(\int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx\) [1082]

Optimal. Leaf size=290 \[ \frac {(A b-a B) (b d-a e)^6 (a+b x)^{11}}{11 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{12}}{12 b^8}+\frac {3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{14}}{14 b^8}+\frac {e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{15}}{3 b^8}+\frac {3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{16}}{16 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{17}}{17 b^8}+\frac {B e^6 (a+b x)^{18}}{18 b^8} \]

[Out]

1/11*(A*b-B*a)*(-a*e+b*d)^6*(b*x+a)^11/b^8+1/12*(-a*e+b*d)^5*(6*A*b*e-7*B*a*e+B*b*d)*(b*x+a)^12/b^8+3/13*e*(-a
*e+b*d)^4*(5*A*b*e-7*B*a*e+2*B*b*d)*(b*x+a)^13/b^8+5/14*e^2*(-a*e+b*d)^3*(4*A*b*e-7*B*a*e+3*B*b*d)*(b*x+a)^14/
b^8+1/3*e^3*(-a*e+b*d)^2*(3*A*b*e-7*B*a*e+4*B*b*d)*(b*x+a)^15/b^8+3/16*e^4*(-a*e+b*d)*(2*A*b*e-7*B*a*e+5*B*b*d
)*(b*x+a)^16/b^8+1/17*e^5*(A*b*e-7*B*a*e+6*B*b*d)*(b*x+a)^17/b^8+1/18*B*e^6*(b*x+a)^18/b^8

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Rubi [A]
time = 1.13, antiderivative size = 290, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} \frac {e^5 (a+b x)^{17} (-7 a B e+A b e+6 b B d)}{17 b^8}+\frac {3 e^4 (a+b x)^{16} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{16 b^8}+\frac {e^3 (a+b x)^{15} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{3 b^8}+\frac {5 e^2 (a+b x)^{14} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{14 b^8}+\frac {3 e (a+b x)^{13} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{13 b^8}+\frac {(a+b x)^{12} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{12 b^8}+\frac {(a+b x)^{11} (A b-a B) (b d-a e)^6}{11 b^8}+\frac {B e^6 (a+b x)^{18}}{18 b^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^11)/(11*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^12)/(
12*b^8) + (3*e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (5*e^2*(b*d - a*e)^3*(3*b*
B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^14)/(14*b^8) + (e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^1
5)/(3*b^8) + (3*e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^16)/(16*b^8) + (e^5*(6*b*B*d + A*b*e -
7*a*B*e)*(a + b*x)^17)/(17*b^8) + (B*e^6*(a + b*x)^18)/(18*b^8)

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx &=\int \left (\frac {(A b-a B) (b d-a e)^6 (a+b x)^{10}}{b^7}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{11}}{b^7}+\frac {3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{12}}{b^7}+\frac {5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{13}}{b^7}+\frac {5 e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{14}}{b^7}+\frac {3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{15}}{b^7}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{16}}{b^7}+\frac {B e^6 (a+b x)^{17}}{b^7}\right ) \, dx\\ &=\frac {(A b-a B) (b d-a e)^6 (a+b x)^{11}}{11 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{12}}{12 b^8}+\frac {3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{14}}{14 b^8}+\frac {e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{15}}{3 b^8}+\frac {3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{16}}{16 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{17}}{17 b^8}+\frac {B e^6 (a+b x)^{18}}{18 b^8}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1788\) vs. \(2(290)=580\).
time = 0.46, size = 1788, normalized size = 6.17 \begin {gather*} a^{10} A d^6 x+\frac {1}{2} a^9 d^5 (10 A b d+a B d+6 a A e) x^2+\frac {1}{3} a^8 d^4 \left (2 a B d (5 b d+3 a e)+15 A \left (3 b^2 d^2+4 a b d e+a^2 e^2\right )\right ) x^3+\frac {5}{4} a^7 d^3 \left (3 a B d \left (3 b^2 d^2+4 a b d e+a^2 e^2\right )+A \left (24 b^3 d^3+54 a b^2 d^2 e+30 a^2 b d e^2+4 a^3 e^3\right )\right ) x^4+a^6 d^2 \left (2 a B d \left (12 b^3 d^3+27 a b^2 d^2 e+15 a^2 b d e^2+2 a^3 e^3\right )+A \left (42 b^4 d^4+144 a b^3 d^3 e+135 a^2 b^2 d^2 e^2+40 a^3 b d e^3+3 a^4 e^4\right )\right ) x^5+\frac {1}{6} a^5 d \left (5 a B d \left (42 b^4 d^4+144 a b^3 d^3 e+135 a^2 b^2 d^2 e^2+40 a^3 b d e^3+3 a^4 e^4\right )+6 A \left (42 b^5 d^5+210 a b^4 d^4 e+300 a^2 b^3 d^3 e^2+150 a^3 b^2 d^2 e^3+25 a^4 b d e^4+a^5 e^5\right )\right ) x^6+\frac {1}{7} a^4 \left (6 a B d \left (42 b^5 d^5+210 a b^4 d^4 e+300 a^2 b^3 d^3 e^2+150 a^3 b^2 d^2 e^3+25 a^4 b d e^4+a^5 e^5\right )+A \left (210 b^6 d^6+1512 a b^5 d^5 e+3150 a^2 b^4 d^4 e^2+2400 a^3 b^3 d^3 e^3+675 a^4 b^2 d^2 e^4+60 a^5 b d e^5+a^6 e^6\right )\right ) x^7+\frac {1}{8} a^3 \left (10 A b \left (12 b^6 d^6+126 a b^5 d^5 e+378 a^2 b^4 d^4 e^2+420 a^3 b^3 d^3 e^3+180 a^4 b^2 d^2 e^4+27 a^5 b d e^5+a^6 e^6\right )+a B \left (210 b^6 d^6+1512 a b^5 d^5 e+3150 a^2 b^4 d^4 e^2+2400 a^3 b^3 d^3 e^3+675 a^4 b^2 d^2 e^4+60 a^5 b d e^5+a^6 e^6\right )\right ) x^8+\frac {5}{9} a^2 b \left (9 A b \left (b^6 d^6+16 a b^5 d^5 e+70 a^2 b^4 d^4 e^2+112 a^3 b^3 d^3 e^3+70 a^4 b^2 d^2 e^4+16 a^5 b d e^5+a^6 e^6\right )+2 a B \left (12 b^6 d^6+126 a b^5 d^5 e+378 a^2 b^4 d^4 e^2+420 a^3 b^3 d^3 e^3+180 a^4 b^2 d^2 e^4+27 a^5 b d e^5+a^6 e^6\right )\right ) x^9+\frac {1}{2} a b^2 \left (9 a B \left (b^6 d^6+16 a b^5 d^5 e+70 a^2 b^4 d^4 e^2+112 a^3 b^3 d^3 e^3+70 a^4 b^2 d^2 e^4+16 a^5 b d e^5+a^6 e^6\right )+2 A b \left (b^6 d^6+27 a b^5 d^5 e+180 a^2 b^4 d^4 e^2+420 a^3 b^3 d^3 e^3+378 a^4 b^2 d^2 e^4+126 a^5 b d e^5+12 a^6 e^6\right )\right ) x^{10}+\frac {1}{11} b^3 \left (10 a B \left (b^6 d^6+27 a b^5 d^5 e+180 a^2 b^4 d^4 e^2+420 a^3 b^3 d^3 e^3+378 a^4 b^2 d^2 e^4+126 a^5 b d e^5+12 a^6 e^6\right )+A b \left (b^6 d^6+60 a b^5 d^5 e+675 a^2 b^4 d^4 e^2+2400 a^3 b^3 d^3 e^3+3150 a^4 b^2 d^2 e^4+1512 a^5 b d e^5+210 a^6 e^6\right )\right ) x^{11}+\frac {1}{12} b^4 \left (210 a^6 B e^6+252 a^5 b e^5 (6 B d+A e)+630 a^4 b^2 d e^4 (5 B d+2 A e)+600 a^3 b^3 d^2 e^3 (4 B d+3 A e)+225 a^2 b^4 d^3 e^2 (3 B d+4 A e)+30 a b^5 d^4 e (2 B d+5 A e)+b^6 d^5 (B d+6 A e)\right ) x^{12}+\frac {1}{13} b^5 e \left (252 a^5 B e^5+210 a^4 b e^4 (6 B d+A e)+360 a^3 b^2 d e^3 (5 B d+2 A e)+225 a^2 b^3 d^2 e^2 (4 B d+3 A e)+50 a b^4 d^3 e (3 B d+4 A e)+3 b^5 d^4 (2 B d+5 A e)\right ) x^{13}+\frac {5}{14} b^6 e^2 \left (42 a^4 B e^4+24 a^3 b e^3 (6 B d+A e)+27 a^2 b^2 d e^2 (5 B d+2 A e)+10 a b^3 d^2 e (4 B d+3 A e)+b^4 d^3 (3 B d+4 A e)\right ) x^{14}+\frac {1}{3} b^7 e^3 \left (24 a^3 B e^3+9 a^2 b e^2 (6 B d+A e)+6 a b^2 d e (5 B d+2 A e)+b^3 d^2 (4 B d+3 A e)\right ) x^{15}+\frac {1}{16} b^8 e^4 \left (45 a^2 B e^2+10 a b e (6 B d+A e)+3 b^2 d (5 B d+2 A e)\right ) x^{16}+\frac {1}{17} b^9 e^5 (6 b B d+A b e+10 a B e) x^{17}+\frac {1}{18} b^{10} B e^6 x^{18} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)^10*(A + B*x)*(d + e*x)^6,x]

[Out]

a^10*A*d^6*x + (a^9*d^5*(10*A*b*d + a*B*d + 6*a*A*e)*x^2)/2 + (a^8*d^4*(2*a*B*d*(5*b*d + 3*a*e) + 15*A*(3*b^2*
d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + (5*a^7*d^3*(3*a*B*d*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + A*(24*b^3*d^3 + 5
4*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + a^6*d^2*(2*a*B*d*(12*b^3*d^3 + 27*a*b^2*d^2*e + 15*a^2*b
*d*e^2 + 2*a^3*e^3) + A*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4))*x^5
+ (a^5*d*(5*a*B*d*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4) + 6*A*(42
*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + (
a^4*(6*a*B*d*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*
e^5) + A*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 +
60*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + (a^3*(10*A*b*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^
3*b^3*d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6) + a*B*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a
^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 + a^6*e^6))*x^8)/8 + (5*a^2*b*(9*
A*b*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5
+ a^6*e^6) + 2*a*B*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 180*a^4*b^2*d^
2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6))*x^9)/9 + (a*b^2*(9*a*B*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e^2 + 112
*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5 + a^6*e^6) + 2*A*b*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*
b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 12*a^6*e^6))*x^10)/2 + (b^3*(10*a*
B*(b^6*d^6 + 27*a*b^5*d^5*e + 180*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 378*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^
5 + 12*a^6*e^6) + A*b*(b^6*d^6 + 60*a*b^5*d^5*e + 675*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 3150*a^4*b^2*d^
2*e^4 + 1512*a^5*b*d*e^5 + 210*a^6*e^6))*x^11)/11 + (b^4*(210*a^6*B*e^6 + 252*a^5*b*e^5*(6*B*d + A*e) + 630*a^
4*b^2*d*e^4*(5*B*d + 2*A*e) + 600*a^3*b^3*d^2*e^3*(4*B*d + 3*A*e) + 225*a^2*b^4*d^3*e^2*(3*B*d + 4*A*e) + 30*a
*b^5*d^4*e*(2*B*d + 5*A*e) + b^6*d^5*(B*d + 6*A*e))*x^12)/12 + (b^5*e*(252*a^5*B*e^5 + 210*a^4*b*e^4*(6*B*d +
A*e) + 360*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 225*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 50*a*b^4*d^3*e*(3*B*d + 4*A*e
) + 3*b^5*d^4*(2*B*d + 5*A*e))*x^13)/13 + (5*b^6*e^2*(42*a^4*B*e^4 + 24*a^3*b*e^3*(6*B*d + A*e) + 27*a^2*b^2*d
*e^2*(5*B*d + 2*A*e) + 10*a*b^3*d^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^14)/14 + (b^7*e^3*(24*a^3*B
*e^3 + 9*a^2*b*e^2*(6*B*d + A*e) + 6*a*b^2*d*e*(5*B*d + 2*A*e) + b^3*d^2*(4*B*d + 3*A*e))*x^15)/3 + (b^8*e^4*(
45*a^2*B*e^2 + 10*a*b*e*(6*B*d + A*e) + 3*b^2*d*(5*B*d + 2*A*e))*x^16)/16 + (b^9*e^5*(6*b*B*d + A*b*e + 10*a*B
*e)*x^17)/17 + (b^10*B*e^6*x^18)/18

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1904\) vs. \(2(274)=548\).
time = 0.08, size = 1905, normalized size = 6.57

method	result	size
default	\(\text {Expression too large to display}\)	\(1905\)
norman	\(\text {Expression too large to display}\)	\(2032\)
gosper	\(\text {Expression too large to display}\)	\(2408\)
risch	\(\text {Expression too large to display}\)	\(2408\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)*(e*x+d)^6,x,method=_RETURNVERBOSE)

[Out]

1/18*b^10*B*e^6*x^18+1/17*((A*b^10+10*B*a*b^9)*e^6+6*b^10*B*d*e^5)*x^17+1/16*((10*A*a*b^9+45*B*a^2*b^8)*e^6+6*
(A*b^10+10*B*a*b^9)*d*e^5+15*b^10*B*d^2*e^4)*x^16+1/15*((45*A*a^2*b^8+120*B*a^3*b^7)*e^6+6*(10*A*a*b^9+45*B*a^
2*b^8)*d*e^5+15*(A*b^10+10*B*a*b^9)*d^2*e^4+20*b^10*B*d^3*e^3)*x^15+1/14*((120*A*a^3*b^7+210*B*a^4*b^6)*e^6+6*
(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^5+15*(10*A*a*b^9+45*B*a^2*b^8)*d^2*e^4+20*(A*b^10+10*B*a*b^9)*d^3*e^3+15*b^10
*B*d^4*e^2)*x^14+1/13*((210*A*a^4*b^6+252*B*a^5*b^5)*e^6+6*(120*A*a^3*b^7+210*B*a^4*b^6)*d*e^5+15*(45*A*a^2*b^
8+120*B*a^3*b^7)*d^2*e^4+20*(10*A*a*b^9+45*B*a^2*b^8)*d^3*e^3+15*(A*b^10+10*B*a*b^9)*d^4*e^2+6*b^10*B*d^5*e)*x
^13+1/12*((252*A*a^5*b^5+210*B*a^6*b^4)*e^6+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^5+15*(120*A*a^3*b^7+210*B*a^4*
b^6)*d^2*e^4+20*(45*A*a^2*b^8+120*B*a^3*b^7)*d^3*e^3+15*(10*A*a*b^9+45*B*a^2*b^8)*d^4*e^2+6*(A*b^10+10*B*a*b^9
)*d^5*e+b^10*B*d^6)*x^12+1/11*((210*A*a^6*b^4+120*B*a^7*b^3)*e^6+6*(252*A*a^5*b^5+210*B*a^6*b^4)*d*e^5+15*(210
*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^4+20*(120*A*a^3*b^7+210*B*a^4*b^6)*d^3*e^3+15*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4
*e^2+6*(10*A*a*b^9+45*B*a^2*b^8)*d^5*e+(A*b^10+10*B*a*b^9)*d^6)*x^11+1/10*((120*A*a^7*b^3+45*B*a^8*b^2)*e^6+6*
(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^5+15*(252*A*a^5*b^5+210*B*a^6*b^4)*d^2*e^4+20*(210*A*a^4*b^6+252*B*a^5*b^5)*
d^3*e^3+15*(120*A*a^3*b^7+210*B*a^4*b^6)*d^4*e^2+6*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e+(10*A*a*b^9+45*B*a^2*b^8
)*d^6)*x^10+1/9*((45*A*a^8*b^2+10*B*a^9*b)*e^6+6*(120*A*a^7*b^3+45*B*a^8*b^2)*d*e^5+15*(210*A*a^6*b^4+120*B*a^
7*b^3)*d^2*e^4+20*(252*A*a^5*b^5+210*B*a^6*b^4)*d^3*e^3+15*(210*A*a^4*b^6+252*B*a^5*b^5)*d^4*e^2+6*(120*A*a^3*
b^7+210*B*a^4*b^6)*d^5*e+(45*A*a^2*b^8+120*B*a^3*b^7)*d^6)*x^9+1/8*((10*A*a^9*b+B*a^10)*e^6+6*(45*A*a^8*b^2+10
*B*a^9*b)*d*e^5+15*(120*A*a^7*b^3+45*B*a^8*b^2)*d^2*e^4+20*(210*A*a^6*b^4+120*B*a^7*b^3)*d^3*e^3+15*(252*A*a^5
*b^5+210*B*a^6*b^4)*d^4*e^2+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d^5*e+(120*A*a^3*b^7+210*B*a^4*b^6)*d^6)*x^8+1/7*(
a^10*A*e^6+6*(10*A*a^9*b+B*a^10)*d*e^5+15*(45*A*a^8*b^2+10*B*a^9*b)*d^2*e^4+20*(120*A*a^7*b^3+45*B*a^8*b^2)*d^
3*e^3+15*(210*A*a^6*b^4+120*B*a^7*b^3)*d^4*e^2+6*(252*A*a^5*b^5+210*B*a^6*b^4)*d^5*e+(210*A*a^4*b^6+252*B*a^5*
b^5)*d^6)*x^7+1/6*(6*a^10*A*d*e^5+15*(10*A*a^9*b+B*a^10)*d^2*e^4+20*(45*A*a^8*b^2+10*B*a^9*b)*d^3*e^3+15*(120*
A*a^7*b^3+45*B*a^8*b^2)*d^4*e^2+6*(210*A*a^6*b^4+120*B*a^7*b^3)*d^5*e+(252*A*a^5*b^5+210*B*a^6*b^4)*d^6)*x^6+1
/5*(15*a^10*A*d^2*e^4+20*(10*A*a^9*b+B*a^10)*d^3*e^3+15*(45*A*a^8*b^2+10*B*a^9*b)*d^4*e^2+6*(120*A*a^7*b^3+45*
B*a^8*b^2)*d^5*e+(210*A*a^6*b^4+120*B*a^7*b^3)*d^6)*x^5+1/4*(20*a^10*A*d^3*e^3+15*(10*A*a^9*b+B*a^10)*d^4*e^2+
6*(45*A*a^8*b^2+10*B*a^9*b)*d^5*e+(120*A*a^7*b^3+45*B*a^8*b^2)*d^6)*x^4+1/3*(15*a^10*A*d^4*e^2+6*(10*A*a^9*b+B
*a^10)*d^5*e+(45*A*a^8*b^2+10*B*a^9*b)*d^6)*x^3+1/2*(6*a^10*A*d^5*e+(10*A*a^9*b+B*a^10)*d^6)*x^2+a^10*A*d^6*x

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1962 vs. \(2 (288) = 576\).
time = 0.33, size = 1962, normalized size = 6.77 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)*(e*x+d)^6,x, algorithm="maxima")

[Out]

1/18*B*b^10*x^18*e^6 + A*a^10*d^6*x + 1/17*(6*B*b^10*d*e^5 + 10*B*a*b^9*e^6 + A*b^10*e^6)*x^17 + 1/16*(15*B*b^
10*d^2*e^4 + 45*B*a^2*b^8*e^6 + 10*A*a*b^9*e^6 + 6*(10*B*a*b^9*e^5 + A*b^10*e^5)*d)*x^16 + 1/3*(4*B*b^10*d^3*e
^3 + 24*B*a^3*b^7*e^6 + 9*A*a^2*b^8*e^6 + 3*(10*B*a*b^9*e^4 + A*b^10*e^4)*d^2 + 6*(9*B*a^2*b^8*e^5 + 2*A*a*b^9
*e^5)*d)*x^15 + 5/14*(3*B*b^10*d^4*e^2 + 42*B*a^4*b^6*e^6 + 24*A*a^3*b^7*e^6 + 4*(10*B*a*b^9*e^3 + A*b^10*e^3)
*d^3 + 15*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d^2 + 18*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d)*x^14 + 1/13*(6*B*b
^10*d^5*e + 252*B*a^5*b^5*e^6 + 210*A*a^4*b^6*e^6 + 15*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^4 + 100*(9*B*a^2*b^8*e^
3 + 2*A*a*b^9*e^3)*d^3 + 225*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d^2 + 180*(7*B*a^4*b^6*e^5 + 4*A*a^3*b^7*e^5)
*d)*x^13 + 1/12*(B*b^10*d^6 + 210*B*a^6*b^4*e^6 + 252*A*a^5*b^5*e^6 + 6*(10*B*a*b^9*e + A*b^10*e)*d^5 + 75*(9*
B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^4 + 300*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^3 + 450*(7*B*a^4*b^6*e^4 + 4*A*
a^3*b^7*e^4)*d^2 + 252*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d)*x^12 + 1/11*(120*B*a^7*b^3*e^6 + 210*A*a^6*b^4*e
^6 + (10*B*a*b^9 + A*b^10)*d^6 + 30*(9*B*a^2*b^8*e + 2*A*a*b^9*e)*d^5 + 225*(8*B*a^3*b^7*e^2 + 3*A*a^2*b^8*e^2
)*d^4 + 600*(7*B*a^4*b^6*e^3 + 4*A*a^3*b^7*e^3)*d^3 + 630*(6*B*a^5*b^5*e^4 + 5*A*a^4*b^6*e^4)*d^2 + 252*(5*B*a
^6*b^4*e^5 + 6*A*a^5*b^5*e^5)*d)*x^11 + 1/2*(9*B*a^8*b^2*e^6 + 24*A*a^7*b^3*e^6 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^
6 + 18*(8*B*a^3*b^7*e + 3*A*a^2*b^8*e)*d^5 + 90*(7*B*a^4*b^6*e^2 + 4*A*a^3*b^7*e^2)*d^4 + 168*(6*B*a^5*b^5*e^3
+ 5*A*a^4*b^6*e^3)*d^3 + 126*(5*B*a^6*b^4*e^4 + 6*A*a^5*b^5*e^4)*d^2 + 36*(4*B*a^7*b^3*e^5 + 7*A*a^6*b^4*e^5)
*d)*x^10 + 5/9*(2*B*a^9*b*e^6 + 9*A*a^8*b^2*e^6 + 3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6 + 36*(7*B*a^4*b^6*e + 4*A*
a^3*b^7*e)*d^5 + 126*(6*B*a^5*b^5*e^2 + 5*A*a^4*b^6*e^2)*d^4 + 168*(5*B*a^6*b^4*e^3 + 6*A*a^5*b^5*e^3)*d^3 + 9
0*(4*B*a^7*b^3*e^4 + 7*A*a^6*b^4*e^4)*d^2 + 18*(3*B*a^8*b^2*e^5 + 8*A*a^7*b^3*e^5)*d)*x^9 + 1/8*(B*a^10*e^6 +
10*A*a^9*b*e^6 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6 + 252*(6*B*a^5*b^5*e + 5*A*a^4*b^6*e)*d^5 + 630*(5*B*a^6*b
^4*e^2 + 6*A*a^5*b^5*e^2)*d^4 + 600*(4*B*a^7*b^3*e^3 + 7*A*a^6*b^4*e^3)*d^3 + 225*(3*B*a^8*b^2*e^4 + 8*A*a^7*b
^3*e^4)*d^2 + 30*(2*B*a^9*b*e^5 + 9*A*a^8*b^2*e^5)*d)*x^8 + 1/7*(A*a^10*e^6 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d
^6 + 252*(5*B*a^6*b^4*e + 6*A*a^5*b^5*e)*d^5 + 450*(4*B*a^7*b^3*e^2 + 7*A*a^6*b^4*e^2)*d^4 + 300*(3*B*a^8*b^2*
e^3 + 8*A*a^7*b^3*e^3)*d^3 + 75*(2*B*a^9*b*e^4 + 9*A*a^8*b^2*e^4)*d^2 + 6*(B*a^10*e^5 + 10*A*a^9*b*e^5)*d)*x^7
+ 1/6*(6*A*a^10*d*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6 + 180*(4*B*a^7*b^3*e + 7*A*a^6*b^4*e)*d^5 + 225*(3
*B*a^8*b^2*e^2 + 8*A*a^7*b^3*e^2)*d^4 + 100*(2*B*a^9*b*e^3 + 9*A*a^8*b^2*e^3)*d^3 + 15*(B*a^10*e^4 + 10*A*a^9*
b*e^4)*d^2)*x^6 + (3*A*a^10*d^2*e^4 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6 + 18*(3*B*a^8*b^2*e + 8*A*a^7*b^3*e)*d
^5 + 15*(2*B*a^9*b*e^2 + 9*A*a^8*b^2*e^2)*d^4 + 4*(B*a^10*e^3 + 10*A*a^9*b*e^3)*d^3)*x^5 + 5/4*(4*A*a^10*d^3*e
^3 + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^6 + 6*(2*B*a^9*b*e + 9*A*a^8*b^2*e)*d^5 + 3*(B*a^10*e^2 + 10*A*a^9*b*e^2)
*d^4)*x^4 + 1/3*(15*A*a^10*d^4*e^2 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^6 + 6*(B*a^10*e + 10*A*a^9*b*e)*d^5)*x^3 +
1/2*(6*A*a^10*d^5*e + (B*a^10 + 10*A*a^9*b)*d^6)*x^2

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1914 vs. \(2 (288) = 576\).
time = 0.88, size = 1914, normalized size = 6.60 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)*(e*x+d)^6,x, algorithm="fricas")

[Out]

1/12*B*b^10*d^6*x^12 + A*a^10*d^6*x + 1/11*(10*B*a*b^9 + A*b^10)*d^6*x^11 + 1/2*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*
x^10 + 5/3*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^9 + 15/4*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x^8 + 6*(6*B*a^5*b^5 + 5
*A*a^4*b^6)*d^6*x^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^6*x^6 + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^6*x^5 + 15/4*(3*
B*a^8*b^2 + 8*A*a^7*b^3)*d^6*x^4 + 5/3*(2*B*a^9*b + 9*A*a^8*b^2)*d^6*x^3 + 1/2*(B*a^10 + 10*A*a^9*b)*d^6*x^2 +
1/2450448*(136136*B*b^10*x^18 + 350064*A*a^10*x^7 + 144144*(10*B*a*b^9 + A*b^10)*x^17 + 765765*(9*B*a^2*b^8 +
2*A*a*b^9)*x^16 + 2450448*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^15 + 5250960*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^14 + 79168
32*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^13 + 8576568*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^12 + 6683040*(4*B*a^7*b^3 + 7*A*a^
6*b^4)*x^11 + 3675672*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^10 + 1361360*(2*B*a^9*b + 9*A*a^8*b^2)*x^9 + 306306*(B*a^1
0 + 10*A*a^9*b)*x^8)*e^6 + 1/136136*(48048*B*b^10*d*x^17 + 136136*A*a^10*d*x^6 + 51051*(10*B*a*b^9 + A*b^10)*d
*x^16 + 272272*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^15 + 875160*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^14 + 1884960*(7*B*a^4
*b^6 + 4*A*a^3*b^7)*d*x^13 + 2858856*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^12 + 3118752*(5*B*a^6*b^4 + 6*A*a^5*b^5)*
d*x^11 + 2450448*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*x^10 + 1361360*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^9 + 510510*(2*B*
a^9*b + 9*A*a^8*b^2)*d*x^8 + 116688*(B*a^10 + 10*A*a^9*b)*d*x^7)*e^5 + 1/16016*(15015*B*b^10*d^2*x^16 + 48048*
A*a^10*d^2*x^5 + 16016*(10*B*a*b^9 + A*b^10)*d^2*x^15 + 85800*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^14 + 277200*(8*B
*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^13 + 600600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^12 + 917280*(6*B*a^5*b^5 + 5*A*a^4
*b^6)*d^2*x^11 + 1009008*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^10 + 800800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x^9 + 4
50450*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x^8 + 171600*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*x^7 + 40040*(B*a^10 + 10*A*a^
9*b)*d^2*x^6)*e^4 + 1/3003*(4004*B*b^10*d^3*x^15 + 15015*A*a^10*d^3*x^4 + 4290*(10*B*a*b^9 + A*b^10)*d^3*x^14
+ 23100*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^13 + 75075*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x^12 + 163800*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^3*x^11 + 252252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^10 + 280280*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3
*x^9 + 225225*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x^8 + 128700*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*x^7 + 50050*(2*B*a^
9*b + 9*A*a^8*b^2)*d^3*x^6 + 12012*(B*a^10 + 10*A*a^9*b)*d^3*x^5)*e^3 + 5/4004*(858*B*b^10*d^4*x^14 + 4004*A*a
^10*d^4*x^3 + 924*(10*B*a*b^9 + A*b^10)*d^4*x^13 + 5005*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^12 + 16380*(8*B*a^3*b^
7 + 3*A*a^2*b^8)*d^4*x^11 + 36036*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^10 + 56056*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4
*x^9 + 63063*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x^8 + 51480*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*x^7 + 30030*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d^4*x^6 + 12012*(2*B*a^9*b + 9*A*a^8*b^2)*d^4*x^5 + 3003*(B*a^10 + 10*A*a^9*b)*d^4*x^4)*e^2
+ 1/286*(132*B*b^10*d^5*x^13 + 858*A*a^10*d^5*x^2 + 143*(10*B*a*b^9 + A*b^10)*d^5*x^12 + 780*(9*B*a^2*b^8 + 2
*A*a*b^9)*d^5*x^11 + 2574*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^10 + 5720*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^9 + 90
09*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x^8 + 10296*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*x^7 + 8580*(4*B*a^7*b^3 + 7*A*a
^6*b^4)*d^5*x^6 + 5148*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^5*x^5 + 2145*(2*B*a^9*b + 9*A*a^8*b^2)*d^5*x^4 + 572*(B*a
^10 + 10*A*a^9*b)*d^5*x^3)*e

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 2424 vs. \(2 (296) = 592\).
time = 0.20, size = 2424, normalized size = 8.36 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**10*(B*x+A)*(e*x+d)**6,x)

[Out]

A*a**10*d**6*x + B*b**10*e**6*x**18/18 + x**17*(A*b**10*e**6/17 + 10*B*a*b**9*e**6/17 + 6*B*b**10*d*e**5/17) +
x**16*(5*A*a*b**9*e**6/8 + 3*A*b**10*d*e**5/8 + 45*B*a**2*b**8*e**6/16 + 15*B*a*b**9*d*e**5/4 + 15*B*b**10*d*
*2*e**4/16) + x**15*(3*A*a**2*b**8*e**6 + 4*A*a*b**9*d*e**5 + A*b**10*d**2*e**4 + 8*B*a**3*b**7*e**6 + 18*B*a*
*2*b**8*d*e**5 + 10*B*a*b**9*d**2*e**4 + 4*B*b**10*d**3*e**3/3) + x**14*(60*A*a**3*b**7*e**6/7 + 135*A*a**2*b*
*8*d*e**5/7 + 75*A*a*b**9*d**2*e**4/7 + 10*A*b**10*d**3*e**3/7 + 15*B*a**4*b**6*e**6 + 360*B*a**3*b**7*d*e**5/
7 + 675*B*a**2*b**8*d**2*e**4/14 + 100*B*a*b**9*d**3*e**3/7 + 15*B*b**10*d**4*e**2/14) + x**13*(210*A*a**4*b**
6*e**6/13 + 720*A*a**3*b**7*d*e**5/13 + 675*A*a**2*b**8*d**2*e**4/13 + 200*A*a*b**9*d**3*e**3/13 + 15*A*b**10*
d**4*e**2/13 + 252*B*a**5*b**5*e**6/13 + 1260*B*a**4*b**6*d*e**5/13 + 1800*B*a**3*b**7*d**2*e**4/13 + 900*B*a*
*2*b**8*d**3*e**3/13 + 150*B*a*b**9*d**4*e**2/13 + 6*B*b**10*d**5*e/13) + x**12*(21*A*a**5*b**5*e**6 + 105*A*a
**4*b**6*d*e**5 + 150*A*a**3*b**7*d**2*e**4 + 75*A*a**2*b**8*d**3*e**3 + 25*A*a*b**9*d**4*e**2/2 + A*b**10*d**
5*e/2 + 35*B*a**6*b**4*e**6/2 + 126*B*a**5*b**5*d*e**5 + 525*B*a**4*b**6*d**2*e**4/2 + 200*B*a**3*b**7*d**3*e*
*3 + 225*B*a**2*b**8*d**4*e**2/4 + 5*B*a*b**9*d**5*e + B*b**10*d**6/12) + x**11*(210*A*a**6*b**4*e**6/11 + 151
2*A*a**5*b**5*d*e**5/11 + 3150*A*a**4*b**6*d**2*e**4/11 + 2400*A*a**3*b**7*d**3*e**3/11 + 675*A*a**2*b**8*d**4
*e**2/11 + 60*A*a*b**9*d**5*e/11 + A*b**10*d**6/11 + 120*B*a**7*b**3*e**6/11 + 1260*B*a**6*b**4*d*e**5/11 + 37
80*B*a**5*b**5*d**2*e**4/11 + 4200*B*a**4*b**6*d**3*e**3/11 + 1800*B*a**3*b**7*d**4*e**2/11 + 270*B*a**2*b**8*
d**5*e/11 + 10*B*a*b**9*d**6/11) + x**10*(12*A*a**7*b**3*e**6 + 126*A*a**6*b**4*d*e**5 + 378*A*a**5*b**5*d**2*
e**4 + 420*A*a**4*b**6*d**3*e**3 + 180*A*a**3*b**7*d**4*e**2 + 27*A*a**2*b**8*d**5*e + A*a*b**9*d**6 + 9*B*a**
8*b**2*e**6/2 + 72*B*a**7*b**3*d*e**5 + 315*B*a**6*b**4*d**2*e**4 + 504*B*a**5*b**5*d**3*e**3 + 315*B*a**4*b**
6*d**4*e**2 + 72*B*a**3*b**7*d**5*e + 9*B*a**2*b**8*d**6/2) + x**9*(5*A*a**8*b**2*e**6 + 80*A*a**7*b**3*d*e**5
+ 350*A*a**6*b**4*d**2*e**4 + 560*A*a**5*b**5*d**3*e**3 + 350*A*a**4*b**6*d**4*e**2 + 80*A*a**3*b**7*d**5*e +
5*A*a**2*b**8*d**6 + 10*B*a**9*b*e**6/9 + 30*B*a**8*b**2*d*e**5 + 200*B*a**7*b**3*d**2*e**4 + 1400*B*a**6*b**
4*d**3*e**3/3 + 420*B*a**5*b**5*d**4*e**2 + 140*B*a**4*b**6*d**5*e + 40*B*a**3*b**7*d**6/3) + x**8*(5*A*a**9*b
*e**6/4 + 135*A*a**8*b**2*d*e**5/4 + 225*A*a**7*b**3*d**2*e**4 + 525*A*a**6*b**4*d**3*e**3 + 945*A*a**5*b**5*d
**4*e**2/2 + 315*A*a**4*b**6*d**5*e/2 + 15*A*a**3*b**7*d**6 + B*a**10*e**6/8 + 15*B*a**9*b*d*e**5/2 + 675*B*a*
*8*b**2*d**2*e**4/8 + 300*B*a**7*b**3*d**3*e**3 + 1575*B*a**6*b**4*d**4*e**2/4 + 189*B*a**5*b**5*d**5*e + 105*
B*a**4*b**6*d**6/4) + x**7*(A*a**10*e**6/7 + 60*A*a**9*b*d*e**5/7 + 675*A*a**8*b**2*d**2*e**4/7 + 2400*A*a**7*
b**3*d**3*e**3/7 + 450*A*a**6*b**4*d**4*e**2 + 216*A*a**5*b**5*d**5*e + 30*A*a**4*b**6*d**6 + 6*B*a**10*d*e**5
/7 + 150*B*a**9*b*d**2*e**4/7 + 900*B*a**8*b**2*d**3*e**3/7 + 1800*B*a**7*b**3*d**4*e**2/7 + 180*B*a**6*b**4*d
**5*e + 36*B*a**5*b**5*d**6) + x**6*(A*a**10*d*e**5 + 25*A*a**9*b*d**2*e**4 + 150*A*a**8*b**2*d**3*e**3 + 300*
A*a**7*b**3*d**4*e**2 + 210*A*a**6*b**4*d**5*e + 42*A*a**5*b**5*d**6 + 5*B*a**10*d**2*e**4/2 + 100*B*a**9*b*d*
*3*e**3/3 + 225*B*a**8*b**2*d**4*e**2/2 + 120*B*a**7*b**3*d**5*e + 35*B*a**6*b**4*d**6) + x**5*(3*A*a**10*d**2
*e**4 + 40*A*a**9*b*d**3*e**3 + 135*A*a**8*b**2*d**4*e**2 + 144*A*a**7*b**3*d**5*e + 42*A*a**6*b**4*d**6 + 4*B
*a**10*d**3*e**3 + 30*B*a**9*b*d**4*e**2 + 54*B*a**8*b**2*d**5*e + 24*B*a**7*b**3*d**6) + x**4*(5*A*a**10*d**3
*e**3 + 75*A*a**9*b*d**4*e**2/2 + 135*A*a**8*b**2*d**5*e/2 + 30*A*a**7*b**3*d**6 + 15*B*a**10*d**4*e**2/4 + 15
*B*a**9*b*d**5*e + 45*B*a**8*b**2*d**6/4) + x**3*(5*A*a**10*d**4*e**2 + 20*A*a**9*b*d**5*e + 15*A*a**8*b**2*d*
*6 + 2*B*a**10*d**5*e + 10*B*a**9*b*d**6/3) + x**2*(3*A*a**10*d**5*e + 5*A*a**9*b*d**6 + B*a**10*d**6/2)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 2319 vs. \(2 (288) = 576\).
time = 1.05, size = 2319, normalized size = 8.00 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)*(e*x+d)^6,x, algorithm="giac")

[Out]

1/18*B*b^10*x^18*e^6 + 6/17*B*b^10*d*x^17*e^5 + 15/16*B*b^10*d^2*x^16*e^4 + 4/3*B*b^10*d^3*x^15*e^3 + 15/14*B*
b^10*d^4*x^14*e^2 + 6/13*B*b^10*d^5*x^13*e + 1/12*B*b^10*d^6*x^12 + 10/17*B*a*b^9*x^17*e^6 + 1/17*A*b^10*x^17*
e^6 + 15/4*B*a*b^9*d*x^16*e^5 + 3/8*A*b^10*d*x^16*e^5 + 10*B*a*b^9*d^2*x^15*e^4 + A*b^10*d^2*x^15*e^4 + 100/7*
B*a*b^9*d^3*x^14*e^3 + 10/7*A*b^10*d^3*x^14*e^3 + 150/13*B*a*b^9*d^4*x^13*e^2 + 15/13*A*b^10*d^4*x^13*e^2 + 5*
B*a*b^9*d^5*x^12*e + 1/2*A*b^10*d^5*x^12*e + 10/11*B*a*b^9*d^6*x^11 + 1/11*A*b^10*d^6*x^11 + 45/16*B*a^2*b^8*x
^16*e^6 + 5/8*A*a*b^9*x^16*e^6 + 18*B*a^2*b^8*d*x^15*e^5 + 4*A*a*b^9*d*x^15*e^5 + 675/14*B*a^2*b^8*d^2*x^14*e^
4 + 75/7*A*a*b^9*d^2*x^14*e^4 + 900/13*B*a^2*b^8*d^3*x^13*e^3 + 200/13*A*a*b^9*d^3*x^13*e^3 + 225/4*B*a^2*b^8*
d^4*x^12*e^2 + 25/2*A*a*b^9*d^4*x^12*e^2 + 270/11*B*a^2*b^8*d^5*x^11*e + 60/11*A*a*b^9*d^5*x^11*e + 9/2*B*a^2*
b^8*d^6*x^10 + A*a*b^9*d^6*x^10 + 8*B*a^3*b^7*x^15*e^6 + 3*A*a^2*b^8*x^15*e^6 + 360/7*B*a^3*b^7*d*x^14*e^5 + 1
35/7*A*a^2*b^8*d*x^14*e^5 + 1800/13*B*a^3*b^7*d^2*x^13*e^4 + 675/13*A*a^2*b^8*d^2*x^13*e^4 + 200*B*a^3*b^7*d^3
*x^12*e^3 + 75*A*a^2*b^8*d^3*x^12*e^3 + 1800/11*B*a^3*b^7*d^4*x^11*e^2 + 675/11*A*a^2*b^8*d^4*x^11*e^2 + 72*B*
a^3*b^7*d^5*x^10*e + 27*A*a^2*b^8*d^5*x^10*e + 40/3*B*a^3*b^7*d^6*x^9 + 5*A*a^2*b^8*d^6*x^9 + 15*B*a^4*b^6*x^1
4*e^6 + 60/7*A*a^3*b^7*x^14*e^6 + 1260/13*B*a^4*b^6*d*x^13*e^5 + 720/13*A*a^3*b^7*d*x^13*e^5 + 525/2*B*a^4*b^6
*d^2*x^12*e^4 + 150*A*a^3*b^7*d^2*x^12*e^4 + 4200/11*B*a^4*b^6*d^3*x^11*e^3 + 2400/11*A*a^3*b^7*d^3*x^11*e^3 +
315*B*a^4*b^6*d^4*x^10*e^2 + 180*A*a^3*b^7*d^4*x^10*e^2 + 140*B*a^4*b^6*d^5*x^9*e + 80*A*a^3*b^7*d^5*x^9*e +
105/4*B*a^4*b^6*d^6*x^8 + 15*A*a^3*b^7*d^6*x^8 + 252/13*B*a^5*b^5*x^13*e^6 + 210/13*A*a^4*b^6*x^13*e^6 + 126*B
*a^5*b^5*d*x^12*e^5 + 105*A*a^4*b^6*d*x^12*e^5 + 3780/11*B*a^5*b^5*d^2*x^11*e^4 + 3150/11*A*a^4*b^6*d^2*x^11*e
^4 + 504*B*a^5*b^5*d^3*x^10*e^3 + 420*A*a^4*b^6*d^3*x^10*e^3 + 420*B*a^5*b^5*d^4*x^9*e^2 + 350*A*a^4*b^6*d^4*x
^9*e^2 + 189*B*a^5*b^5*d^5*x^8*e + 315/2*A*a^4*b^6*d^5*x^8*e + 36*B*a^5*b^5*d^6*x^7 + 30*A*a^4*b^6*d^6*x^7 + 3
5/2*B*a^6*b^4*x^12*e^6 + 21*A*a^5*b^5*x^12*e^6 + 1260/11*B*a^6*b^4*d*x^11*e^5 + 1512/11*A*a^5*b^5*d*x^11*e^5 +
315*B*a^6*b^4*d^2*x^10*e^4 + 378*A*a^5*b^5*d^2*x^10*e^4 + 1400/3*B*a^6*b^4*d^3*x^9*e^3 + 560*A*a^5*b^5*d^3*x^
9*e^3 + 1575/4*B*a^6*b^4*d^4*x^8*e^2 + 945/2*A*a^5*b^5*d^4*x^8*e^2 + 180*B*a^6*b^4*d^5*x^7*e + 216*A*a^5*b^5*d
^5*x^7*e + 35*B*a^6*b^4*d^6*x^6 + 42*A*a^5*b^5*d^6*x^6 + 120/11*B*a^7*b^3*x^11*e^6 + 210/11*A*a^6*b^4*x^11*e^6
+ 72*B*a^7*b^3*d*x^10*e^5 + 126*A*a^6*b^4*d*x^10*e^5 + 200*B*a^7*b^3*d^2*x^9*e^4 + 350*A*a^6*b^4*d^2*x^9*e^4
+ 300*B*a^7*b^3*d^3*x^8*e^3 + 525*A*a^6*b^4*d^3*x^8*e^3 + 1800/7*B*a^7*b^3*d^4*x^7*e^2 + 450*A*a^6*b^4*d^4*x^7
*e^2 + 120*B*a^7*b^3*d^5*x^6*e + 210*A*a^6*b^4*d^5*x^6*e + 24*B*a^7*b^3*d^6*x^5 + 42*A*a^6*b^4*d^6*x^5 + 9/2*B
*a^8*b^2*x^10*e^6 + 12*A*a^7*b^3*x^10*e^6 + 30*B*a^8*b^2*d*x^9*e^5 + 80*A*a^7*b^3*d*x^9*e^5 + 675/8*B*a^8*b^2*
d^2*x^8*e^4 + 225*A*a^7*b^3*d^2*x^8*e^4 + 900/7*B*a^8*b^2*d^3*x^7*e^3 + 2400/7*A*a^7*b^3*d^3*x^7*e^3 + 225/2*B
*a^8*b^2*d^4*x^6*e^2 + 300*A*a^7*b^3*d^4*x^6*e^2 + 54*B*a^8*b^2*d^5*x^5*e + 144*A*a^7*b^3*d^5*x^5*e + 45/4*B*a
^8*b^2*d^6*x^4 + 30*A*a^7*b^3*d^6*x^4 + 10/9*B*a^9*b*x^9*e^6 + 5*A*a^8*b^2*x^9*e^6 + 15/2*B*a^9*b*d*x^8*e^5 +
135/4*A*a^8*b^2*d*x^8*e^5 + 150/7*B*a^9*b*d^2*x^7*e^4 + 675/7*A*a^8*b^2*d^2*x^7*e^4 + 100/3*B*a^9*b*d^3*x^6*e^
3 + 150*A*a^8*b^2*d^3*x^6*e^3 + 30*B*a^9*b*d^4*x^5*e^2 + 135*A*a^8*b^2*d^4*x^5*e^2 + 15*B*a^9*b*d^5*x^4*e + 13
5/2*A*a^8*b^2*d^5*x^4*e + 10/3*B*a^9*b*d^6*x^3 + 15*A*a^8*b^2*d^6*x^3 + 1/8*B*a^10*x^8*e^6 + 5/4*A*a^9*b*x^8*e
^6 + 6/7*B*a^10*d*x^7*e^5 + 60/7*A*a^9*b*d*x^7*e^5 + 5/2*B*a^10*d^2*x^6*e^4 + 25*A*a^9*b*d^2*x^6*e^4 + 4*B*a^1
0*d^3*x^5*e^3 + 40*A*a^9*b*d^3*x^5*e^3 + 15/4*B*a^10*d^4*x^4*e^2 + 75/2*A*a^9*b*d^4*x^4*e^2 + 2*B*a^10*d^5*x^3
*e + 20*A*a^9*b*d^5*x^3*e + 1/2*B*a^10*d^6*x^2 + 5*A*a^9*b*d^6*x^2 + 1/7*A*a^10*x^7*e^6 + A*a^10*d*x^6*e^5 + 3
*A*a^10*d^2*x^5*e^4 + 5*A*a^10*d^3*x^4*e^3 + 5*A*a^10*d^4*x^3*e^2 + 3*A*a^10*d^5*x^2*e + A*a^10*d^6*x

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Mupad [B]
time = 1.74, size = 2001, normalized size = 6.90 \begin {gather*} x^6\,\left (\frac {5\,B\,a^{10}\,d^2\,e^4}{2}+A\,a^{10}\,d\,e^5+\frac {100\,B\,a^9\,b\,d^3\,e^3}{3}+25\,A\,a^9\,b\,d^2\,e^4+\frac {225\,B\,a^8\,b^2\,d^4\,e^2}{2}+150\,A\,a^8\,b^2\,d^3\,e^3+120\,B\,a^7\,b^3\,d^5\,e+300\,A\,a^7\,b^3\,d^4\,e^2+35\,B\,a^6\,b^4\,d^6+210\,A\,a^6\,b^4\,d^5\,e+42\,A\,a^5\,b^5\,d^6\right )+x^{13}\,\left (\frac {252\,B\,a^5\,b^5\,e^6}{13}+\frac {1260\,B\,a^4\,b^6\,d\,e^5}{13}+\frac {210\,A\,a^4\,b^6\,e^6}{13}+\frac {1800\,B\,a^3\,b^7\,d^2\,e^4}{13}+\frac {720\,A\,a^3\,b^7\,d\,e^5}{13}+\frac {900\,B\,a^2\,b^8\,d^3\,e^3}{13}+\frac {675\,A\,a^2\,b^8\,d^2\,e^4}{13}+\frac {150\,B\,a\,b^9\,d^4\,e^2}{13}+\frac {200\,A\,a\,b^9\,d^3\,e^3}{13}+\frac {6\,B\,b^{10}\,d^5\,e}{13}+\frac {15\,A\,b^{10}\,d^4\,e^2}{13}\right )+x^5\,\left (4\,B\,a^{10}\,d^3\,e^3+3\,A\,a^{10}\,d^2\,e^4+30\,B\,a^9\,b\,d^4\,e^2+40\,A\,a^9\,b\,d^3\,e^3+54\,B\,a^8\,b^2\,d^5\,e+135\,A\,a^8\,b^2\,d^4\,e^2+24\,B\,a^7\,b^3\,d^6+144\,A\,a^7\,b^3\,d^5\,e+42\,A\,a^6\,b^4\,d^6\right )+x^{14}\,\left (15\,B\,a^4\,b^6\,e^6+\frac {360\,B\,a^3\,b^7\,d\,e^5}{7}+\frac {60\,A\,a^3\,b^7\,e^6}{7}+\frac {675\,B\,a^2\,b^8\,d^2\,e^4}{14}+\frac {135\,A\,a^2\,b^8\,d\,e^5}{7}+\frac {100\,B\,a\,b^9\,d^3\,e^3}{7}+\frac {75\,A\,a\,b^9\,d^2\,e^4}{7}+\frac {15\,B\,b^{10}\,d^4\,e^2}{14}+\frac {10\,A\,b^{10}\,d^3\,e^3}{7}\right )+x^7\,\left (\frac {6\,B\,a^{10}\,d\,e^5}{7}+\frac {A\,a^{10}\,e^6}{7}+\frac {150\,B\,a^9\,b\,d^2\,e^4}{7}+\frac {60\,A\,a^9\,b\,d\,e^5}{7}+\frac {900\,B\,a^8\,b^2\,d^3\,e^3}{7}+\frac {675\,A\,a^8\,b^2\,d^2\,e^4}{7}+\frac {1800\,B\,a^7\,b^3\,d^4\,e^2}{7}+\frac {2400\,A\,a^7\,b^3\,d^3\,e^3}{7}+180\,B\,a^6\,b^4\,d^5\,e+450\,A\,a^6\,b^4\,d^4\,e^2+36\,B\,a^5\,b^5\,d^6+216\,A\,a^5\,b^5\,d^5\,e+30\,A\,a^4\,b^6\,d^6\right )+x^{12}\,\left (\frac {35\,B\,a^6\,b^4\,e^6}{2}+126\,B\,a^5\,b^5\,d\,e^5+21\,A\,a^5\,b^5\,e^6+\frac {525\,B\,a^4\,b^6\,d^2\,e^4}{2}+105\,A\,a^4\,b^6\,d\,e^5+200\,B\,a^3\,b^7\,d^3\,e^3+150\,A\,a^3\,b^7\,d^2\,e^4+\frac {225\,B\,a^2\,b^8\,d^4\,e^2}{4}+75\,A\,a^2\,b^8\,d^3\,e^3+5\,B\,a\,b^9\,d^5\,e+\frac {25\,A\,a\,b^9\,d^4\,e^2}{2}+\frac {B\,b^{10}\,d^6}{12}+\frac {A\,b^{10}\,d^5\,e}{2}\right )+x^4\,\left (\frac {15\,B\,a^{10}\,d^4\,e^2}{4}+5\,A\,a^{10}\,d^3\,e^3+15\,B\,a^9\,b\,d^5\,e+\frac {75\,A\,a^9\,b\,d^4\,e^2}{2}+\frac {45\,B\,a^8\,b^2\,d^6}{4}+\frac {135\,A\,a^8\,b^2\,d^5\,e}{2}+30\,A\,a^7\,b^3\,d^6\right )+x^{15}\,\left (8\,B\,a^3\,b^7\,e^6+18\,B\,a^2\,b^8\,d\,e^5+3\,A\,a^2\,b^8\,e^6+10\,B\,a\,b^9\,d^2\,e^4+4\,A\,a\,b^9\,d\,e^5+\frac {4\,B\,b^{10}\,d^3\,e^3}{3}+A\,b^{10}\,d^2\,e^4\right )+x^8\,\left (\frac {B\,a^{10}\,e^6}{8}+\frac {15\,B\,a^9\,b\,d\,e^5}{2}+\frac {5\,A\,a^9\,b\,e^6}{4}+\frac {675\,B\,a^8\,b^2\,d^2\,e^4}{8}+\frac {135\,A\,a^8\,b^2\,d\,e^5}{4}+300\,B\,a^7\,b^3\,d^3\,e^3+225\,A\,a^7\,b^3\,d^2\,e^4+\frac {1575\,B\,a^6\,b^4\,d^4\,e^2}{4}+525\,A\,a^6\,b^4\,d^3\,e^3+189\,B\,a^5\,b^5\,d^5\,e+\frac {945\,A\,a^5\,b^5\,d^4\,e^2}{2}+\frac {105\,B\,a^4\,b^6\,d^6}{4}+\frac {315\,A\,a^4\,b^6\,d^5\,e}{2}+15\,A\,a^3\,b^7\,d^6\right )+x^{11}\,\left (\frac {120\,B\,a^7\,b^3\,e^6}{11}+\frac {1260\,B\,a^6\,b^4\,d\,e^5}{11}+\frac {210\,A\,a^6\,b^4\,e^6}{11}+\frac {3780\,B\,a^5\,b^5\,d^2\,e^4}{11}+\frac {1512\,A\,a^5\,b^5\,d\,e^5}{11}+\frac {4200\,B\,a^4\,b^6\,d^3\,e^3}{11}+\frac {3150\,A\,a^4\,b^6\,d^2\,e^4}{11}+\frac {1800\,B\,a^3\,b^7\,d^4\,e^2}{11}+\frac {2400\,A\,a^3\,b^7\,d^3\,e^3}{11}+\frac {270\,B\,a^2\,b^8\,d^5\,e}{11}+\frac {675\,A\,a^2\,b^8\,d^4\,e^2}{11}+\frac {10\,B\,a\,b^9\,d^6}{11}+\frac {60\,A\,a\,b^9\,d^5\,e}{11}+\frac {A\,b^{10}\,d^6}{11}\right )+x^{10}\,\left (\frac {9\,B\,a^8\,b^2\,e^6}{2}+72\,B\,a^7\,b^3\,d\,e^5+12\,A\,a^7\,b^3\,e^6+315\,B\,a^6\,b^4\,d^2\,e^4+126\,A\,a^6\,b^4\,d\,e^5+504\,B\,a^5\,b^5\,d^3\,e^3+378\,A\,a^5\,b^5\,d^2\,e^4+315\,B\,a^4\,b^6\,d^4\,e^2+420\,A\,a^4\,b^6\,d^3\,e^3+72\,B\,a^3\,b^7\,d^5\,e+180\,A\,a^3\,b^7\,d^4\,e^2+\frac {9\,B\,a^2\,b^8\,d^6}{2}+27\,A\,a^2\,b^8\,d^5\,e+A\,a\,b^9\,d^6\right )+x^9\,\left (\frac {10\,B\,a^9\,b\,e^6}{9}+30\,B\,a^8\,b^2\,d\,e^5+5\,A\,a^8\,b^2\,e^6+200\,B\,a^7\,b^3\,d^2\,e^4+80\,A\,a^7\,b^3\,d\,e^5+\frac {1400\,B\,a^6\,b^4\,d^3\,e^3}{3}+350\,A\,a^6\,b^4\,d^2\,e^4+420\,B\,a^5\,b^5\,d^4\,e^2+560\,A\,a^5\,b^5\,d^3\,e^3+140\,B\,a^4\,b^6\,d^5\,e+350\,A\,a^4\,b^6\,d^4\,e^2+\frac {40\,B\,a^3\,b^7\,d^6}{3}+80\,A\,a^3\,b^7\,d^5\,e+5\,A\,a^2\,b^8\,d^6\right )+\frac {a^9\,d^5\,x^2\,\left (6\,A\,a\,e+10\,A\,b\,d+B\,a\,d\right )}{2}+\frac {b^9\,e^5\,x^{17}\,\left (A\,b\,e+10\,B\,a\,e+6\,B\,b\,d\right )}{17}+A\,a^{10}\,d^6\,x+\frac {a^8\,d^4\,x^3\,\left (6\,B\,a^2\,d\,e+15\,A\,a^2\,e^2+10\,B\,a\,b\,d^2+60\,A\,a\,b\,d\,e+45\,A\,b^2\,d^2\right )}{3}+\frac {b^8\,e^4\,x^{16}\,\left (45\,B\,a^2\,e^2+60\,B\,a\,b\,d\,e+10\,A\,a\,b\,e^2+15\,B\,b^2\,d^2+6\,A\,b^2\,d\,e\right )}{16}+\frac {B\,b^{10}\,e^6\,x^{18}}{18} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((A + B*x)*(a + b*x)^10*(d + e*x)^6,x)

[Out]

x^6*(A*a^10*d*e^5 + 42*A*a^5*b^5*d^6 + 35*B*a^6*b^4*d^6 + (5*B*a^10*d^2*e^4)/2 + 210*A*a^6*b^4*d^5*e + 25*A*a^
9*b*d^2*e^4 + 120*B*a^7*b^3*d^5*e + (100*B*a^9*b*d^3*e^3)/3 + 300*A*a^7*b^3*d^4*e^2 + 150*A*a^8*b^2*d^3*e^3 +
(225*B*a^8*b^2*d^4*e^2)/2) + x^13*((6*B*b^10*d^5*e)/13 + (210*A*a^4*b^6*e^6)/13 + (252*B*a^5*b^5*e^6)/13 + (15
*A*b^10*d^4*e^2)/13 + (200*A*a*b^9*d^3*e^3)/13 + (720*A*a^3*b^7*d*e^5)/13 + (150*B*a*b^9*d^4*e^2)/13 + (1260*B
*a^4*b^6*d*e^5)/13 + (675*A*a^2*b^8*d^2*e^4)/13 + (900*B*a^2*b^8*d^3*e^3)/13 + (1800*B*a^3*b^7*d^2*e^4)/13) +
x^5*(42*A*a^6*b^4*d^6 + 24*B*a^7*b^3*d^6 + 3*A*a^10*d^2*e^4 + 4*B*a^10*d^3*e^3 + 144*A*a^7*b^3*d^5*e + 40*A*a^
9*b*d^3*e^3 + 54*B*a^8*b^2*d^5*e + 30*B*a^9*b*d^4*e^2 + 135*A*a^8*b^2*d^4*e^2) + x^14*((60*A*a^3*b^7*e^6)/7 +
15*B*a^4*b^6*e^6 + (10*A*b^10*d^3*e^3)/7 + (15*B*b^10*d^4*e^2)/14 + (75*A*a*b^9*d^2*e^4)/7 + (135*A*a^2*b^8*d*
e^5)/7 + (100*B*a*b^9*d^3*e^3)/7 + (360*B*a^3*b^7*d*e^5)/7 + (675*B*a^2*b^8*d^2*e^4)/14) + x^7*((A*a^10*e^6)/7
+ (6*B*a^10*d*e^5)/7 + 30*A*a^4*b^6*d^6 + 36*B*a^5*b^5*d^6 + 216*A*a^5*b^5*d^5*e + 180*B*a^6*b^4*d^5*e + (150
*B*a^9*b*d^2*e^4)/7 + 450*A*a^6*b^4*d^4*e^2 + (2400*A*a^7*b^3*d^3*e^3)/7 + (675*A*a^8*b^2*d^2*e^4)/7 + (1800*B
*a^7*b^3*d^4*e^2)/7 + (900*B*a^8*b^2*d^3*e^3)/7 + (60*A*a^9*b*d*e^5)/7) + x^12*((B*b^10*d^6)/12 + (A*b^10*d^5*
e)/2 + 21*A*a^5*b^5*e^6 + (35*B*a^6*b^4*e^6)/2 + (25*A*a*b^9*d^4*e^2)/2 + 105*A*a^4*b^6*d*e^5 + 126*B*a^5*b^5*
d*e^5 + 75*A*a^2*b^8*d^3*e^3 + 150*A*a^3*b^7*d^2*e^4 + (225*B*a^2*b^8*d^4*e^2)/4 + 200*B*a^3*b^7*d^3*e^3 + (52
5*B*a^4*b^6*d^2*e^4)/2 + 5*B*a*b^9*d^5*e) + x^4*(30*A*a^7*b^3*d^6 + (45*B*a^8*b^2*d^6)/4 + 5*A*a^10*d^3*e^3 +
(15*B*a^10*d^4*e^2)/4 + (135*A*a^8*b^2*d^5*e)/2 + (75*A*a^9*b*d^4*e^2)/2 + 15*B*a^9*b*d^5*e) + x^15*(3*A*a^2*b
^8*e^6 + 8*B*a^3*b^7*e^6 + A*b^10*d^2*e^4 + (4*B*b^10*d^3*e^3)/3 + 10*B*a*b^9*d^2*e^4 + 18*B*a^2*b^8*d*e^5 + 4
*A*a*b^9*d*e^5) + x^8*((B*a^10*e^6)/8 + (5*A*a^9*b*e^6)/4 + 15*A*a^3*b^7*d^6 + (105*B*a^4*b^6*d^6)/4 + (315*A*
a^4*b^6*d^5*e)/2 + (135*A*a^8*b^2*d*e^5)/4 + 189*B*a^5*b^5*d^5*e + (945*A*a^5*b^5*d^4*e^2)/2 + 525*A*a^6*b^4*d
^3*e^3 + 225*A*a^7*b^3*d^2*e^4 + (1575*B*a^6*b^4*d^4*e^2)/4 + 300*B*a^7*b^3*d^3*e^3 + (675*B*a^8*b^2*d^2*e^4)/
8 + (15*B*a^9*b*d*e^5)/2) + x^11*((A*b^10*d^6)/11 + (10*B*a*b^9*d^6)/11 + (210*A*a^6*b^4*e^6)/11 + (120*B*a^7*
b^3*e^6)/11 + (1512*A*a^5*b^5*d*e^5)/11 + (270*B*a^2*b^8*d^5*e)/11 + (1260*B*a^6*b^4*d*e^5)/11 + (675*A*a^2*b^
8*d^4*e^2)/11 + (2400*A*a^3*b^7*d^3*e^3)/11 + (3150*A*a^4*b^6*d^2*e^4)/11 + (1800*B*a^3*b^7*d^4*e^2)/11 + (420
0*B*a^4*b^6*d^3*e^3)/11 + (3780*B*a^5*b^5*d^2*e^4)/11 + (60*A*a*b^9*d^5*e)/11) + x^10*(A*a*b^9*d^6 + 12*A*a^7*
b^3*e^6 + (9*B*a^2*b^8*d^6)/2 + (9*B*a^8*b^2*e^6)/2 + 27*A*a^2*b^8*d^5*e + 126*A*a^6*b^4*d*e^5 + 72*B*a^3*b^7*
d^5*e + 72*B*a^7*b^3*d*e^5 + 180*A*a^3*b^7*d^4*e^2 + 420*A*a^4*b^6*d^3*e^3 + 378*A*a^5*b^5*d^2*e^4 + 315*B*a^4
*b^6*d^4*e^2 + 504*B*a^5*b^5*d^3*e^3 + 315*B*a^6*b^4*d^2*e^4) + x^9*((10*B*a^9*b*e^6)/9 + 5*A*a^2*b^8*d^6 + 5*
A*a^8*b^2*e^6 + (40*B*a^3*b^7*d^6)/3 + 80*A*a^3*b^7*d^5*e + 80*A*a^7*b^3*d*e^5 + 140*B*a^4*b^6*d^5*e + 30*B*a^
8*b^2*d*e^5 + 350*A*a^4*b^6*d^4*e^2 + 560*A*a^5*b^5*d^3*e^3 + 350*A*a^6*b^4*d^2*e^4 + 420*B*a^5*b^5*d^4*e^2 +
(1400*B*a^6*b^4*d^3*e^3)/3 + 200*B*a^7*b^3*d^2*e^4) + (a^9*d^5*x^2*(6*A*a*e + 10*A*b*d + B*a*d))/2 + (b^9*e^5*
x^17*(A*b*e + 10*B*a*e + 6*B*b*d))/17 + A*a^10*d^6*x + (a^8*d^4*x^3*(15*A*a^2*e^2 + 45*A*b^2*d^2 + 10*B*a*b*d^
2 + 6*B*a^2*d*e + 60*A*a*b*d*e))/3 + (b^8*e^4*x^16*(45*B*a^2*e^2 + 15*B*b^2*d^2 + 10*A*a*b*e^2 + 6*A*b^2*d*e +
60*B*a*b*d*e))/16 + (B*b^10*e^6*x^18)/18

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